Theorems · Theorem · linear algebra

mulLeftLinearMap_mul

∀ {l : Type u_1} {m : Type u_2} {n : Type u_3} {o : Type u_4} {R : Type u_5} {A : Type u_6} [inst : Fintype m]
  [inst_1 : Fintype n] [inst_2 : Semiring R] [inst_3 : NonUnitalSemiring A] [inst_4 : Module R A]
  [inst_5 : SMulCommClass R A A] (a : Matrix l m A) (b : Matrix m n A),
  mulLeftLinearMap o R (a * b) = mulLeftLinearMap o R a ∘ₗ mulLeftLinearMap o R b

A version of LinearMap.mulLeft_mul for matrix multiplication.

Defined in

Mathlib.LinearAlgebra.Matrix.Bilinear

Cited by

0 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeFintypeSemiringNonUnitalSemiringModuleSMulCommClass